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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.

Turkel, E.↗
NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗
NASA NTRS1978

User's guide to computer programs JET 5A and CIVM-JET 5B to calculate the large elastic-plastic dynamically-induced deformations of multilayer partial and/or complete structural rings

These structural ring deflections lie essentially in one plane and, hence, are called two-dimensional (2-d). The structural rings may be complete or partial; the former may be regarded as representing a fragment containment ring while the latter may be viewed as a 2-d fragment-deflector structure. These two types of rings may be either free or supported in various ways (pinned-fixed, locally clamped, elastic-foundation supported, mounting-bracket supported, etc.). The initial geometry of each ring may be circular or arbitrarily curved; uniform-thickness or variable-thickness rings may be analyzed. Strain-hardening and strain-rate effects of initially-isotropic material are taken into account. An approximate analysis utilizing kinetic energy and momentum conservation relations is used to predict the after-impact velocities of each fragment and of the impact-affected region of the ring; this procedure is termed the collision-imparted velocity method (CIVM) and is used in the CIVM-JET 5 B program. This imparted-velocity information is used in conjunction with a finite-element structural response computation code to predict the transient, large-deflection, elastic-plastic responses of the ring. Similarly, the equations of motion of each fragment are solved in small steps in time. Provisions are made in the CIVM-JET 5B code to analyze structural ring response to impact attack by from 1 to 3 fragments, each with its own size, mass, translational velocity components, and rotational velocity. The effects of friction between each fragment and the impacted ring are included.

Wu, R. W. H.↗
NASA NTRS1978

Measurement of D-region electron density by partial reflections

Measurements of electron density in the lower ionosphere were made at White Sands Missile Range throughout the STRATCOM VIII launch day using a partial-reflection sounder. Information regarding the sounder's antenna pattern was gained from the passage of the balloon over the array.

Olsen, R. O.↗
NASA NTRS1979

Flight test evaluation of an RAF high altitude partial pressure protective assembly

A partial pressure suit was evaluated during tests in an F-104 and F-15 as a protective garment for emergency descents. The garment is an pressure jerkin and modified anti-g suit combined with an oronasal mask. The garment can be donned and doffed at the aircraft to minimize thermal buildup. The oronasal mask was favored by the pilots due to its immobility on the face during high g-loading. The garment was chosen to provide optimum dexterity for the pilot, which is not available in a full pressure suit, while protecting the pilot at altitudes up to 18,288 meters, during a cabin decompression, and subsequent aircraft descent. During cabin decompressions in the F-104 and F-15, cabin pressure altitude was measured at various aircraft angles of attack, Mach numbers, and altitudes to determine the effect of the aerodynamic slipstream on the cabin altitude.

Ashworth, G. R.↗
NASA NTRS1978

Al-26 and the partial ionization of the solar nebula

It is shown that an even distribution of the amount of Al-26 equal to 10 to the minus tenth power of the amount of H (the amount of Al-26 suggested by scaling from cosmic abundances) will lead to a small but significant partial ionization of the nebular gas. Calculation of the ionization state and consequent magnetic Reynolds number for the solar nebula shows that the presence of Al-26 will result in strong coupling of the gas to magnetic fields. In the absence of Al-26, K-40 will still result in substantial ionization, but the degree of magnetic coupling is much more model dependent.

Consolmagno, G. J.↗
NASA NTRS1978

Stochastic partial differential equations in turbulence related problems

The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

Chow, P.-L.↗
NASA NTRS1979

Energy conserving norms for the solution of hyperbolic systems of partial differential equations

The hyperbolic system of partial differential equations with a real constant square coefficient matrix A is considered. The problem of finding an energy conserving norm for the solution of the system is reduced to the problem of characterizing those matrices appearing in the boundary conditions which satisfy two specific matrix equations. Necessary and sufficient conditions on the coefficient matrix A and the matrices appearing in boundary conditions are derived for an energy conserving norm. The conditions serve as criteria on a given system which determine whether or not the solution will have its energy conserved in some norm. Examples of specific systems and boundary conditions are also provided.

Gunzburger, M. D.↗
NASA NTRS1979

The geometry of the partial realization problem

It is shown that the space of sequences of length n which have an extrapolation of McMillan degree k, and no extrapolations of lower McMillan degree can be given the structure of a differentiable manifold. This approach makes the proof of certain known results on the partial realization problem quite straightforward and makes it possible to establish some important new results as well. A key tool is the fact, proven here, that the set of n by a real Hankel matrices of rank r is a manifold with r+1 connected components.

Brockett, R. W.↗
NASA NTRS1979

On the interweaving of partial cross sections of different parity

Partial cross sections of definite parity, calculated for electronic-rotational energy transfer in the F +H2 collision system, interweave with increasing total angular momentum J. An explanation, in terms of diabatic curve crossings induced by the centrifugal potential in the body-fixed coordinate system, predicts the interweaving to occur only in systems having half-integer J.

Devries, P. L.↗
NASA NTRS1979

A study of partial coherence for identifying interior noise sources and paths on general aviation aircraft

The partial coherence analysis method for noise source/path determination is summarized and the application to a two input, single output system with coherence between the inputs is illustrated. The augmentation of the calculations on a digital computer interfaced with a two channel, real time analyzer is also discussed. The results indicate possible sources of error in the computations and suggest procedures for avoiding these errors.

Howlett, J. T.↗
NASA NTRS1980

Experimental study of flow due to an isolated suction hole and a partially plugged suction slot

Details for construction of a model of a partially plugged, laminar flow control, suction slot and an isolated hole are presented. The experimental wind tunnel facility and instrumentation is described. Preliminary boundary layer velocity profiles (without suction model) are presented and shown to be in good agreement with the Blasius laminar profile. Recommendations for the completion of the study are made. An experimental program for study of transition on a rotating disk is described along with preliminary disturbance amplification rate data.

Goglia, G. L.↗
NASA NTRS1980

Hydroelastic vibration analysis of partially liquid-filled shells using a series representation of the liquid

A series representation of the oscillatory behavior of incompressible nonviscous liquids contained in partially filled elastic tanks is presented. Each term is selected on the basis of hydroelastic vibrations in circular cylindrical tanks. Using a complementary energy principle, the superposition of terms is made to approximately satisfy the liquid-tank interface compatibility. This analysis is applied to the gravity sloshing and hydroelastic vibrations of liquids in hemispherical tanks and in a typical elastic aerospace propellant tank. With only a few series terms retained, the results correlate very well with existing analytical results, NASTRAN-generated analytical results, and experimental test results. Hence, although each term is based on a cylindrical tank geometry, the superposition can be successfully applied to noncylindrical tanks.

Housner, J. M.↗
NASA NTRS1979

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Turkel, E.↗
NASA NTRS1978

A computer program for calculating aerodynamic characteristics of low aspect-ratio wings with partial leading-edge separation

The necessary information for using a computer program to predict distributed and total aerodynamic characteristics for low aspect ratio wings with partial leading-edge separation is presented. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the Quasi-Vortex-Lattice method. The leading edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at midpoints to satisfy the force free condition. The wake behind the trailing edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading and trailing edges. The program is restricted to delta wings with zero thickness and no camber. It is written in FORTRAN language and runs on CDC 6600 computer.

Mehrotra, S. C.↗
NASA NTRS1979

Instructions for the use of the CIVM-Jet 4C finite-strain computer code to calculate the transient structural responses of partial and/or complete arbitrarily-curved rings subjected to fragment impact

The CIVM-JET 4C computer program for the 'finite strain' analysis of 2 d transient structural responses of complete or partial rings and beams subjected to fragment impact stored on tape as a series of individual files. Which subroutines are found in these files are described in detail. All references to the CIVM-JET 4C program are made assuming that the user has a copy of NASA CR-134907 (ASRL TR 154-9) which serves as a user's guide to (1) the CIVM-JET 4B computer code and (2) the CIVM-JET 4C computer code 'with the use of the modified input instructions' attached hereto.

Rodal, J. J. A.↗
NASA NTRS1979

Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations

Elliptic partial differential equations are used to generate a smooth grid that permits a one-to-one mapping in such a way that mesh lines of the same family do not cross. Problems that arise due to lack of clustering at crucial points or intersections of mesh lines at highly acute angles, are examined and various forcing or source terms are used (to correct the problems) that are either compatible with the maximum principle or are so locally controlled that mesh lines do not intersect. Attention is given to various schematics of unclustered grids and grid detail about (highly cambered) airfoils.

Steger, J. L.↗
NASA NTRS1980

Viscosity of multicomponent partially ionized gas mixtures

An approximate method is proposed for predicting the viscosity of partially ionized gas mixtures. This technique expresses the viscosity of a mixture in terms of the viscosities of the individual pure components, is simple in form, and does not require large computer run times or storage. Thus, the technique is suitable for use with complex flowfields and heat-transfer calculations. Results for gas mixtures which are representative of the atmospheres of Jupiter, Earth, and Venus, are presented and it is shown that the results compare favorably with detailed kinetic-theory analyses.

Armaly, B. F.↗